app.R

library(shiny)

# MODULE UI
customInputUI <- function(id) {
  ns <- NS(id)
  verbatimTextOutput(ns("debug"))
}

# MODULE SERVER 
# Render the custom shiny input binding
customInput <- function(input, output, session) {
  # This should return "This is a test" from script.js....?
  output$debug <- renderPrint({ input$testing })
}

ui <- fixedPage(
  h2("Shiny.setInputValue Inside Module"),
  customInputUI("custom_input"),
  
  # This is where we assign the custom binding
  tags$script(src = "script.js")
  
)

server <- function(input, output, session) {
  df <- callModule(customInput, "custom_input")
}

shinyApp(ui, server)

script.js

Shiny.setInputValue('test-testing', "This is a test");